The integration of vision-language modalities has been a significant focus in multimodal learning, traditionally relying on Vision-Language Pretrained Models. However, with the advent of Large Language Models (LLMs), there has been a notable shift towards incorporating LLMs with vision modalities. Following this, the training paradigms for incorporating vision modalities into LLMs have evolved. Initially, the approach was to integrate the modalities through pretraining the modality integrator, named Single-stage Tuning. It has since branched out into methods focusing on performance enhancement, denoted as Two-stage Tuning, and those prioritizing parameter efficiency, referred to as Direct Adaptation. However, existing surveys primarily address the latest Vision Large Language Models (VLLMs) with Two-stage Tuning, leaving a gap in understanding the evolution of training paradigms and their unique parameter-efficient considerations. This paper categorizes and reviews 34 VLLMs from top conferences, journals, and highly cited Arxiv papers, focusing on parameter efficiency during adaptation from the training paradigm perspective. We first introduce the architecture of LLMs and parameter-efficient learning methods, followed by a discussion on vision encoders and a comprehensive taxonomy of modality integrators. We then review three training paradigms and their efficiency considerations, summarizing benchmarks in the VLLM field. To gain deeper insights into their effectiveness in parameter efficiency, we compare and discuss the experimental results of representative models, among which the experiment of the Direct Adaptation paradigm is replicated. Providing insights into recent developments and practical uses, this survey is a vital guide for researchers and practitioners navigating the efficient integration of vision modalities into LLMs.